Started lecture 6 material

Author: LProcopi15

Week 5 - Introduction to Modeling/Lecture5.R

@@ -20,7 +20,6 @@ for (i in 1:ncol(fire)){
 summary(fire$area)
 areabox <- boxplot(fire$area)
 upperwhisk <- areabox$stats[5,]
-
 xtm_fire <- subset(fire, area >= upperwhisk, select = c('FFMC', 'DMC', 'DC', 'ISI', 'temp', 'RH', 'wind', 'rain', 'area'))
 
 ####################
@@ -83,6 +82,7 @@ lm1_ISI <- lm(area~wind, data = high_ISI)
 
 # 5. Determine if there are any correlated attributes
 symnum(cor(high_ISI[c("FFMC", "DMC", "DC", "ISI", "temp", "RH", "wind", "rain")]))
+?symnum
 
 # 6. If there are any correlated attributes add the interaction between them to a new model 
 # Call this model lm2_ISI - RH and temp
@@ -100,13 +100,18 @@ anova(lm1_ISI, lm2_ISI)
 
 #Suppose we want to develop a model to predict the area and also using month and day attributes
 class(fire$month)
+levels(fire$month)
 contrasts(fire$month)
 class(fire$day)
 contrasts(fire$day)
 
+lm(area~temp+month+day, data = fire)
+
 #Get the right dataset
 xtm_fire_withCategorical <- subset(fire, area >= upperwhisk, select = c('FFMC', 'DMC', 'DC', 'ISI', 'temp', 'RH', 'wind', 'rain', 'area','month','day'))
 lm4 <- lm(area~temp+FFMC+wind+(DC+DMC)^2+(ISI+FFMC)^2+(temp+FFMC)^2+month+day, data = xtm_fire_withCategorical)
+summary(lm4)  
+
 
 #Practice problem: is lm4 better than lm3? How do you know?
 
@@ -149,6 +154,7 @@ pmse.lm.train
 
 #Practice question: how does pmse.lm.train compared to the MSE on the training set? Which value better represents the robustness of the model?
 #Hint: use mean((lm.train$residuals)^2) to compute the MSE on training set
+mean((lm.train$residuals)^2)
 
 #####################
 #

Week 6 - Assumptions and Transformations/Lecture6.R

@@ -0,0 +1,65 @@
+fire <- read.csv("C:/Users/Student/Documents/UVA 2016-2017/RWorkshop/Week 5 - Introduction to Modeling/forestfires.csv")
+lm1 <- lm(area~temp, data = xtm_fire)
+lm3 <- lm(area~temp+FFMC+wind+(DC+DMC)^2+(ISI+FFMC)^2+(temp+FFMC)^2, data = xtm_fire)
+
+######################
+#
+# Diagnostic plots
+#
+#####################
+# 1. Residual vs. Fitted: constant variance, no pattern, even scatter about the mean
+# 2. Normal Q-Q: dots are on the line
+# 3. Scale-Location: constant variance, no pattern, even scatter about the mean
+# 4. Residual vs. Leverage: Points outside of Cook's distance are influential points
+par(mfrow=c(2,2))
+plot(lm1, labels.id = NULL)
+par(mfrow=c(1,1))
+# Based on Cook's distance we see that 32 is an influential point
+xtm_fire[32,]
+hist(xtm_fire$area)
+summary(xtm_fire$area)
+
+par(mfrow=c(2,2))
+plot(lm3, labels.id = NULL)
+par(mfrow=c(1,1))
+
+######################
+#
+# Model Comparison
+#
+#####################
+
+# AIC - smaller is better
+AIC(lm1) # 834.4967
+AIC(lm3) # 848.3075
+
+# BIC - smaller is better
+AIC(lm1,k=log(nrow(xtm_fire))) # 840.9733
+AIC(lm3,k=log(nrow(xtm_fire))) # 872.0552
+
+# adj-R2 - closer to 1 is better
+summary(lm1)$adj.r.squared
+summary(lm3)$adj.r.squared
+
+
+######################
+#
+# Transformations and Modeling
+#
+#####################
+
+# Stepwise
+lm.cas2.step<-step(lm.cas2)
+
+# Box-cox
+library(MASS)
+boxcox(lm1) 
+# Value near 0 thus we need to perform a log transform
+
+#The best lambda
+L<-boxcox(accdmg.lm1, plotit = F)$x[which.max(boxcox(accdmg.lm1, plotit = F)$y)] 
+L
+
+# Box-cox transform
+xdmgnd.lm1.boxcox<-lm(ACCDMG^L ~TEMP + TRNSPD + TONS + CARS + HEADEND1,data=xdmgnd)
+summary(xdmgnd.lm1.boxcox)